Question

A farmer had a square piece of land, that he described as y + 7 feet in length and width. It was all planted with corn; except for one small square that was 7 ft. by 7 ft. It was planted with radish. Express the area that is only planted in corn using polynomials.

Answer 1

Answer: Therefore, the area that is only planted in corn can be expressed as the polynomial y^2 + 14y.

Explanation:

The area of the square piece of land is given by the product of its length and width:

Area of square piece of land = (y + 7) * (y + 7)

The area of the small square that was planted with radish is 7 ft. by 7 ft. Therefore, its area is:

Area of small square = 7 * 7 = 49

The area that is only planted in corn is the difference between the area of the square piece of land and the area of the small square that was planted with radish:

Area planted in corn = (y + 7) * (y + 7) - 49

Expanding the expression on the right side, we get:

Area planted in corn = y^2 + 14y + 49 - 49

Simplifying further, we get:

Area planted in corn = y^2 + 14y